# Properties

 Label 405.4.e.r.136.1 Level $405$ Weight $4$ Character 405.136 Analytic conductor $23.896$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$405 = 3^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 405.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$23.8957735523$$ Analytic rank: $$0$$ Dimension: $$6$$ Relative dimension: $$3$$ over $$\Q(\zeta_{3})$$ Coefficient field: 6.0.95327307.1 Defining polynomial: $$x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 85x^{2} - 68x + 16$$ x^6 - 3*x^5 + 20*x^4 - 35*x^3 + 85*x^2 - 68*x + 16 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$3^{3}$$ Twist minimal: no (minimal twist has level 135) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 136.1 Root $$0.500000 + 0.0280269i$$ of defining polynomial Character $$\chi$$ $$=$$ 405.136 Dual form 405.4.e.r.271.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-2.60034 + 4.50391i) q^{2} +(-9.52349 - 16.4952i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-12.2007 + 21.1322i) q^{7} +57.4517 q^{8} +O(q^{10})$$ $$q+(-2.60034 + 4.50391i) q^{2} +(-9.52349 - 16.4952i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-12.2007 + 21.1322i) q^{7} +57.4517 q^{8} -26.0034 q^{10} +(14.4919 - 25.1008i) q^{11} +(32.6960 + 56.6311i) q^{13} +(-63.4517 - 109.902i) q^{14} +(-73.2057 + 126.796i) q^{16} +68.1718 q^{17} +104.424 q^{19} +(47.6174 - 82.4758i) q^{20} +(75.3678 + 130.541i) q^{22} +(77.4033 + 134.067i) q^{23} +(-12.5000 + 21.6506i) q^{25} -340.082 q^{26} +464.772 q^{28} +(102.829 - 178.105i) q^{29} +(9.12485 + 15.8047i) q^{31} +(-150.912 - 261.387i) q^{32} +(-177.269 + 307.040i) q^{34} -122.007 q^{35} -337.613 q^{37} +(-271.538 + 470.317i) q^{38} +(143.629 + 248.773i) q^{40} +(97.9845 + 169.714i) q^{41} +(-167.441 + 290.016i) q^{43} -552.055 q^{44} -805.098 q^{46} +(2.50199 - 4.33358i) q^{47} +(-126.213 - 218.607i) q^{49} +(-65.0084 - 112.598i) q^{50} +(622.759 - 1078.65i) q^{52} -319.965 q^{53} +144.919 q^{55} +(-700.949 + 1214.08i) q^{56} +(534.779 + 926.265i) q^{58} +(-215.305 - 372.920i) q^{59} +(-297.291 + 514.922i) q^{61} -94.9106 q^{62} +398.396 q^{64} +(-163.480 + 283.155i) q^{65} +(-97.9382 - 169.634i) q^{67} +(-649.233 - 1124.50i) q^{68} +(317.258 - 549.508i) q^{70} +425.955 q^{71} +929.193 q^{73} +(877.908 - 1520.58i) q^{74} +(-994.482 - 1722.49i) q^{76} +(353.623 + 612.492i) q^{77} +(-12.2148 + 21.1567i) q^{79} -732.057 q^{80} -1019.17 q^{82} +(272.929 - 472.727i) q^{83} +(170.429 + 295.192i) q^{85} +(-870.805 - 1508.28i) q^{86} +(832.586 - 1442.08i) q^{88} -84.1332 q^{89} -1595.65 q^{91} +(1474.30 - 2553.56i) q^{92} +(13.0120 + 22.5375i) q^{94} +(261.060 + 452.170i) q^{95} +(-413.807 + 716.734i) q^{97} +1312.78 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q - q^{2} - 23 q^{4} + 15 q^{5} - 44 q^{7} + 72 q^{8}+O(q^{10})$$ 6 * q - q^2 - 23 * q^4 + 15 * q^5 - 44 * q^7 + 72 * q^8 $$6 q - q^{2} - 23 q^{4} + 15 q^{5} - 44 q^{7} + 72 q^{8} - 10 q^{10} + 38 q^{11} - 28 q^{13} - 108 q^{14} - 191 q^{16} + 38 q^{17} + 374 q^{19} + 115 q^{20} - 122 q^{22} - 81 q^{23} - 75 q^{25} - 832 q^{26} + 820 q^{28} + 160 q^{29} - 227 q^{31} - 569 q^{32} - 17 q^{34} - 440 q^{35} + 156 q^{37} - 757 q^{38} + 180 q^{40} - 338 q^{41} - 22 q^{43} - 3272 q^{44} - 2850 q^{46} - 472 q^{47} + 197 q^{49} - 25 q^{50} + 1566 q^{52} - 1042 q^{53} + 380 q^{55} - 1254 q^{56} + 2096 q^{58} + 140 q^{59} - 595 q^{61} - 2814 q^{62} - 1836 q^{64} + 140 q^{65} - 878 q^{67} - 3053 q^{68} + 540 q^{70} + 1204 q^{71} + 2588 q^{73} + 2878 q^{74} - 525 q^{76} + 288 q^{77} - 629 q^{79} - 1910 q^{80} - 3364 q^{82} - 1287 q^{83} + 95 q^{85} - 3730 q^{86} + 858 q^{88} - 4308 q^{89} - 880 q^{91} + 1959 q^{92} + 1108 q^{94} + 935 q^{95} - 1392 q^{97} + 5386 q^{98}+O(q^{100})$$ 6 * q - q^2 - 23 * q^4 + 15 * q^5 - 44 * q^7 + 72 * q^8 - 10 * q^10 + 38 * q^11 - 28 * q^13 - 108 * q^14 - 191 * q^16 + 38 * q^17 + 374 * q^19 + 115 * q^20 - 122 * q^22 - 81 * q^23 - 75 * q^25 - 832 * q^26 + 820 * q^28 + 160 * q^29 - 227 * q^31 - 569 * q^32 - 17 * q^34 - 440 * q^35 + 156 * q^37 - 757 * q^38 + 180 * q^40 - 338 * q^41 - 22 * q^43 - 3272 * q^44 - 2850 * q^46 - 472 * q^47 + 197 * q^49 - 25 * q^50 + 1566 * q^52 - 1042 * q^53 + 380 * q^55 - 1254 * q^56 + 2096 * q^58 + 140 * q^59 - 595 * q^61 - 2814 * q^62 - 1836 * q^64 + 140 * q^65 - 878 * q^67 - 3053 * q^68 + 540 * q^70 + 1204 * q^71 + 2588 * q^73 + 2878 * q^74 - 525 * q^76 + 288 * q^77 - 629 * q^79 - 1910 * q^80 - 3364 * q^82 - 1287 * q^83 + 95 * q^85 - 3730 * q^86 + 858 * q^88 - 4308 * q^89 - 880 * q^91 + 1959 * q^92 + 1108 * q^94 + 935 * q^95 - 1392 * q^97 + 5386 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$$.

 $$n$$ $$82$$ $$326$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −2.60034 + 4.50391i −0.919357 + 1.59237i −0.118964 + 0.992899i $$0.537957\pi$$
−0.800393 + 0.599475i $$0.795376\pi$$
$$3$$ 0 0
$$4$$ −9.52349 16.4952i −1.19044 2.06190i
$$5$$ 2.50000 + 4.33013i 0.223607 + 0.387298i
$$6$$ 0 0
$$7$$ −12.2007 + 21.1322i −0.658774 + 1.14103i 0.322159 + 0.946686i $$0.395591\pi$$
−0.980933 + 0.194345i $$0.937742\pi$$
$$8$$ 57.4517 2.53903
$$9$$ 0 0
$$10$$ −26.0034 −0.822298
$$11$$ 14.4919 25.1008i 0.397226 0.688015i −0.596157 0.802868i $$-0.703306\pi$$
0.993383 + 0.114853i $$0.0366397\pi$$
$$12$$ 0 0
$$13$$ 32.6960 + 56.6311i 0.697556 + 1.20820i 0.969311 + 0.245836i $$0.0790625\pi$$
−0.271756 + 0.962366i $$0.587604\pi$$
$$14$$ −63.4517 109.902i −1.21130 2.09803i
$$15$$ 0 0
$$16$$ −73.2057 + 126.796i −1.14384 + 1.98119i
$$17$$ 68.1718 0.972593 0.486296 0.873794i $$-0.338347\pi$$
0.486296 + 0.873794i $$0.338347\pi$$
$$18$$ 0 0
$$19$$ 104.424 1.26087 0.630435 0.776242i $$-0.282876\pi$$
0.630435 + 0.776242i $$0.282876\pi$$
$$20$$ 47.6174 82.4758i 0.532379 0.922108i
$$21$$ 0 0
$$22$$ 75.3678 + 130.541i 0.730385 + 1.26506i
$$23$$ 77.4033 + 134.067i 0.701727 + 1.21543i 0.967860 + 0.251490i $$0.0809205\pi$$
−0.266133 + 0.963936i $$0.585746\pi$$
$$24$$ 0 0
$$25$$ −12.5000 + 21.6506i −0.100000 + 0.173205i
$$26$$ −340.082 −2.56521
$$27$$ 0 0
$$28$$ 464.772 3.13691
$$29$$ 102.829 178.105i 0.658443 1.14046i −0.322576 0.946544i $$-0.604549\pi$$
0.981019 0.193913i $$-0.0621179\pi$$
$$30$$ 0 0
$$31$$ 9.12485 + 15.8047i 0.0528668 + 0.0915680i 0.891248 0.453517i $$-0.149831\pi$$
−0.838381 + 0.545085i $$0.816497\pi$$
$$32$$ −150.912 261.387i −0.833679 1.44397i
$$33$$ 0 0
$$34$$ −177.269 + 307.040i −0.894160 + 1.54873i
$$35$$ −122.007 −0.589226
$$36$$ 0 0
$$37$$ −337.613 −1.50009 −0.750044 0.661387i $$-0.769968\pi$$
−0.750044 + 0.661387i $$0.769968\pi$$
$$38$$ −271.538 + 470.317i −1.15919 + 2.00778i
$$39$$ 0 0
$$40$$ 143.629 + 248.773i 0.567744 + 0.983362i
$$41$$ 97.9845 + 169.714i 0.373234 + 0.646461i 0.990061 0.140638i $$-0.0449154\pi$$
−0.616827 + 0.787099i $$0.711582\pi$$
$$42$$ 0 0
$$43$$ −167.441 + 290.016i −0.593826 + 1.02854i 0.399886 + 0.916565i $$0.369050\pi$$
−0.993711 + 0.111971i $$0.964284\pi$$
$$44$$ −552.055 −1.89149
$$45$$ 0 0
$$46$$ −805.098 −2.58055
$$47$$ 2.50199 4.33358i 0.00776496 0.0134493i −0.862117 0.506710i $$-0.830862\pi$$
0.869882 + 0.493260i $$0.164195\pi$$
$$48$$ 0 0
$$49$$ −126.213 218.607i −0.367967 0.637338i
$$50$$ −65.0084 112.598i −0.183871 0.318475i
$$51$$ 0 0
$$52$$ 622.759 1078.65i 1.66079 2.87657i
$$53$$ −319.965 −0.829256 −0.414628 0.909991i $$-0.636088\pi$$
−0.414628 + 0.909991i $$0.636088\pi$$
$$54$$ 0 0
$$55$$ 144.919 0.355289
$$56$$ −700.949 + 1214.08i −1.67265 + 2.89711i
$$57$$ 0 0
$$58$$ 534.779 + 926.265i 1.21069 + 2.09697i
$$59$$ −215.305 372.920i −0.475091 0.822882i 0.524502 0.851409i $$-0.324251\pi$$
−0.999593 + 0.0285276i $$0.990918\pi$$
$$60$$ 0 0
$$61$$ −297.291 + 514.922i −0.624002 + 1.08080i 0.364730 + 0.931113i $$0.381161\pi$$
−0.988733 + 0.149691i $$0.952172\pi$$
$$62$$ −94.9106 −0.194414
$$63$$ 0 0
$$64$$ 398.396 0.778118
$$65$$ −163.480 + 283.155i −0.311956 + 0.540324i
$$66$$ 0 0
$$67$$ −97.9382 169.634i −0.178583 0.309315i 0.762812 0.646620i $$-0.223818\pi$$
−0.941395 + 0.337305i $$0.890485\pi$$
$$68$$ −649.233 1124.50i −1.15781 2.00538i
$$69$$ 0 0
$$70$$ 317.258 549.508i 0.541709 0.938267i
$$71$$ 425.955 0.711994 0.355997 0.934487i $$-0.384141\pi$$
0.355997 + 0.934487i $$0.384141\pi$$
$$72$$ 0 0
$$73$$ 929.193 1.48978 0.744889 0.667188i $$-0.232502\pi$$
0.744889 + 0.667188i $$0.232502\pi$$
$$74$$ 877.908 1520.58i 1.37912 2.38870i
$$75$$ 0 0
$$76$$ −994.482 1722.49i −1.50099 2.59978i
$$77$$ 353.623 + 612.492i 0.523364 + 0.906493i
$$78$$ 0 0
$$79$$ −12.2148 + 21.1567i −0.0173959 + 0.0301305i −0.874592 0.484859i $$-0.838871\pi$$
0.857196 + 0.514990i $$0.172204\pi$$
$$80$$ −732.057 −1.02308
$$81$$ 0 0
$$82$$ −1019.17 −1.37254
$$83$$ 272.929 472.727i 0.360938 0.625164i −0.627177 0.778877i $$-0.715790\pi$$
0.988116 + 0.153713i $$0.0491231\pi$$
$$84$$ 0 0
$$85$$ 170.429 + 295.192i 0.217478 + 0.376684i
$$86$$ −870.805 1508.28i −1.09188 1.89118i
$$87$$ 0 0
$$88$$ 832.586 1442.08i 1.00857 1.74689i
$$89$$ −84.1332 −0.100203 −0.0501017 0.998744i $$-0.515955\pi$$
−0.0501017 + 0.998744i $$0.515955\pi$$
$$90$$ 0 0
$$91$$ −1595.65 −1.83813
$$92$$ 1474.30 2553.56i 1.67072 2.89377i
$$93$$ 0 0
$$94$$ 13.0120 + 22.5375i 0.0142775 + 0.0247294i
$$95$$ 261.060 + 452.170i 0.281939 + 0.488333i
$$96$$ 0 0
$$97$$ −413.807 + 716.734i −0.433152 + 0.750241i −0.997143 0.0755403i $$-0.975932\pi$$
0.563991 + 0.825781i $$0.309265\pi$$
$$98$$ 1312.78 1.35317
$$99$$ 0 0
$$100$$ 476.174 0.476174
$$101$$ −411.788 + 713.238i −0.405688 + 0.702671i −0.994401 0.105670i $$-0.966301\pi$$
0.588714 + 0.808342i $$0.299635\pi$$
$$102$$ 0 0
$$103$$ −585.595 1014.28i −0.560198 0.970291i −0.997479 0.0709659i $$-0.977392\pi$$
0.437281 0.899325i $$-0.355941\pi$$
$$104$$ 1878.44 + 3253.55i 1.77111 + 3.06766i
$$105$$ 0 0
$$106$$ 832.016 1441.09i 0.762383 1.32049i
$$107$$ 1023.21 0.924460 0.462230 0.886760i $$-0.347049\pi$$
0.462230 + 0.886760i $$0.347049\pi$$
$$108$$ 0 0
$$109$$ −403.647 −0.354700 −0.177350 0.984148i $$-0.556753\pi$$
−0.177350 + 0.984148i $$0.556753\pi$$
$$110$$ −376.839 + 652.704i −0.326638 + 0.565754i
$$111$$ 0 0
$$112$$ −1786.32 3093.99i −1.50706 2.61031i
$$113$$ −541.102 937.216i −0.450465 0.780229i 0.547950 0.836511i $$-0.315409\pi$$
−0.998415 + 0.0562825i $$0.982075\pi$$
$$114$$ 0 0
$$115$$ −387.017 + 670.333i −0.313822 + 0.543555i
$$116$$ −3917.16 −3.13534
$$117$$ 0 0
$$118$$ 2239.46 1.74711
$$119$$ −831.741 + 1440.62i −0.640719 + 1.10976i
$$120$$ 0 0
$$121$$ 245.468 + 425.162i 0.184423 + 0.319431i
$$122$$ −1546.11 2677.94i −1.14736 1.98729i
$$123$$ 0 0
$$124$$ 173.801 301.032i 0.125869 0.218012i
$$125$$ −125.000 −0.0894427
$$126$$ 0 0
$$127$$ −774.132 −0.540890 −0.270445 0.962735i $$-0.587171\pi$$
−0.270445 + 0.962735i $$0.587171\pi$$
$$128$$ 171.332 296.756i 0.118311 0.204920i
$$129$$ 0 0
$$130$$ −850.204 1472.60i −0.573599 0.993503i
$$131$$ 607.019 + 1051.39i 0.404851 + 0.701222i 0.994304 0.106580i $$-0.0339901\pi$$
−0.589453 + 0.807802i $$0.700657\pi$$
$$132$$ 0 0
$$133$$ −1274.04 + 2206.71i −0.830629 + 1.43869i
$$134$$ 1018.69 0.656726
$$135$$ 0 0
$$136$$ 3916.58 2.46944
$$137$$ −1150.07 + 1991.99i −0.717207 + 1.24224i 0.244895 + 0.969550i $$0.421247\pi$$
−0.962102 + 0.272690i $$0.912087\pi$$
$$138$$ 0 0
$$139$$ 677.963 + 1174.27i 0.413698 + 0.716546i 0.995291 0.0969339i $$-0.0309035\pi$$
−0.581593 + 0.813480i $$0.697570\pi$$
$$140$$ 1161.93 + 2012.52i 0.701435 + 1.21492i
$$141$$ 0 0
$$142$$ −1107.63 + 1918.47i −0.654577 + 1.13376i
$$143$$ 1895.31 1.10835
$$144$$ 0 0
$$145$$ 1028.29 0.588929
$$146$$ −2416.21 + 4185.00i −1.36964 + 2.37228i
$$147$$ 0 0
$$148$$ 3215.26 + 5568.99i 1.78576 + 3.09303i
$$149$$ −129.923 225.032i −0.0714340 0.123727i 0.828096 0.560586i $$-0.189424\pi$$
−0.899530 + 0.436859i $$0.856091\pi$$
$$150$$ 0 0
$$151$$ 254.152 440.204i 0.136971 0.237240i −0.789378 0.613908i $$-0.789597\pi$$
0.926349 + 0.376667i $$0.122930\pi$$
$$152$$ 5999.34 3.20139
$$153$$ 0 0
$$154$$ −3678.15 −1.92463
$$155$$ −45.6242 + 79.0235i −0.0236428 + 0.0409504i
$$156$$ 0 0
$$157$$ 11.6526 + 20.1829i 0.00592342 + 0.0102597i 0.868972 0.494861i $$-0.164781\pi$$
−0.863049 + 0.505121i $$0.831448\pi$$
$$158$$ −63.5252 110.029i −0.0319860 0.0554014i
$$159$$ 0 0
$$160$$ 754.560 1306.94i 0.372833 0.645765i
$$161$$ −3777.49 −1.84912
$$162$$ 0 0
$$163$$ −4032.10 −1.93754 −0.968769 0.247964i $$-0.920238\pi$$
−0.968769 + 0.247964i $$0.920238\pi$$
$$164$$ 1866.31 3232.54i 0.888623 1.53914i
$$165$$ 0 0
$$166$$ 1419.42 + 2458.50i 0.663663 + 1.14950i
$$167$$ 335.955 + 581.892i 0.155671 + 0.269630i 0.933303 0.359090i $$-0.116913\pi$$
−0.777632 + 0.628719i $$0.783579\pi$$
$$168$$ 0 0
$$169$$ −1039.55 + 1800.56i −0.473169 + 0.819552i
$$170$$ −1772.69 −0.799761
$$171$$ 0 0
$$172$$ 6378.49 2.82765
$$173$$ −816.764 + 1414.68i −0.358944 + 0.621710i −0.987785 0.155825i $$-0.950197\pi$$
0.628840 + 0.777534i $$0.283530\pi$$
$$174$$ 0 0
$$175$$ −305.017 528.305i −0.131755 0.228206i
$$176$$ 2121.78 + 3675.04i 0.908725 + 1.57396i
$$177$$ 0 0
$$178$$ 218.775 378.929i 0.0921227 0.159561i
$$179$$ 341.260 0.142497 0.0712485 0.997459i $$-0.477302\pi$$
0.0712485 + 0.997459i $$0.477302\pi$$
$$180$$ 0 0
$$181$$ −1695.92 −0.696447 −0.348223 0.937412i $$-0.613215\pi$$
−0.348223 + 0.937412i $$0.613215\pi$$
$$182$$ 4149.23 7186.67i 1.68990 2.92699i
$$183$$ 0 0
$$184$$ 4446.95 + 7702.34i 1.78170 + 3.08600i
$$185$$ −844.033 1461.91i −0.335430 0.580982i
$$186$$ 0 0
$$187$$ 987.941 1711.16i 0.386339 0.669159i
$$188$$ −95.3107 −0.0369747
$$189$$ 0 0
$$190$$ −2715.38 −1.03681
$$191$$ 363.226 629.125i 0.137603 0.238335i −0.788986 0.614411i $$-0.789394\pi$$
0.926589 + 0.376076i $$0.122727\pi$$
$$192$$ 0 0
$$193$$ −2123.63 3678.24i −0.792032 1.37184i −0.924707 0.380681i $$-0.875690\pi$$
0.132674 0.991160i $$-0.457644\pi$$
$$194$$ −2152.07 3727.50i −0.796442 1.37948i
$$195$$ 0 0
$$196$$ −2403.97 + 4163.80i −0.876082 + 1.51742i
$$197$$ 2678.52 0.968713 0.484357 0.874871i $$-0.339054\pi$$
0.484357 + 0.874871i $$0.339054\pi$$
$$198$$ 0 0
$$199$$ 1486.48 0.529517 0.264759 0.964315i $$-0.414708\pi$$
0.264759 + 0.964315i $$0.414708\pi$$
$$200$$ −718.146 + 1243.87i −0.253903 + 0.439773i
$$201$$ 0 0
$$202$$ −2141.57 3709.31i −0.745944 1.29201i
$$203$$ 2509.16 + 4346.00i 0.867530 + 1.50261i
$$204$$ 0 0
$$205$$ −489.923 + 848.571i −0.166915 + 0.289106i
$$206$$ 6090.97 2.06009
$$207$$ 0 0
$$208$$ −9574.12 −3.19157
$$209$$ 1513.31 2621.13i 0.500850 0.867498i
$$210$$ 0 0
$$211$$ 2413.71 + 4180.66i 0.787519 + 1.36402i 0.927483 + 0.373866i $$0.121968\pi$$
−0.139964 + 0.990157i $$0.544699\pi$$
$$212$$ 3047.18 + 5277.87i 0.987176 + 1.70984i
$$213$$ 0 0
$$214$$ −2660.68 + 4608.44i −0.849909 + 1.47209i
$$215$$ −1674.41 −0.531134
$$216$$ 0 0
$$217$$ −445.317 −0.139309
$$218$$ 1049.62 1817.99i 0.326096 0.564815i
$$219$$ 0 0
$$220$$ −1380.14 2390.47i −0.422949 0.732570i
$$221$$ 2228.94 + 3860.64i 0.678438 + 1.17509i
$$222$$ 0 0
$$223$$ −1387.24 + 2402.77i −0.416576 + 0.721532i −0.995593 0.0937845i $$-0.970104\pi$$
0.579016 + 0.815316i $$0.303437\pi$$
$$224$$ 7364.91 2.19683
$$225$$ 0 0
$$226$$ 5628.19 1.65655
$$227$$ 2550.67 4417.89i 0.745788 1.29174i −0.204038 0.978963i $$-0.565407\pi$$
0.949826 0.312779i $$-0.101260\pi$$
$$228$$ 0 0
$$229$$ 2048.91 + 3548.82i 0.591249 + 1.02407i 0.994065 + 0.108792i $$0.0346983\pi$$
−0.402816 + 0.915281i $$0.631968\pi$$
$$230$$ −2012.75 3486.18i −0.577028 0.999443i
$$231$$ 0 0
$$232$$ 5907.69 10232.4i 1.67181 2.89565i
$$233$$ 357.613 0.100549 0.0502747 0.998735i $$-0.483990\pi$$
0.0502747 + 0.998735i $$0.483990\pi$$
$$234$$ 0 0
$$235$$ 25.0199 0.00694519
$$236$$ −4100.91 + 7102.99i −1.13113 + 1.95918i
$$237$$ 0 0
$$238$$ −4325.61 7492.18i −1.17810 2.04053i
$$239$$ 175.841 + 304.566i 0.0475909 + 0.0824298i 0.888840 0.458219i $$-0.151512\pi$$
−0.841249 + 0.540648i $$0.818179\pi$$
$$240$$ 0 0
$$241$$ 3082.76 5339.51i 0.823976 1.42717i −0.0787225 0.996897i $$-0.525084\pi$$
0.902699 0.430273i $$-0.141583\pi$$
$$242$$ −2553.19 −0.678204
$$243$$ 0 0
$$244$$ 11325.0 2.97134
$$245$$ 631.064 1093.03i 0.164560 0.285026i
$$246$$ 0 0
$$247$$ 3414.25 + 5913.65i 0.879528 + 1.52339i
$$248$$ 524.238 + 908.006i 0.134230 + 0.232494i
$$249$$ 0 0
$$250$$ 325.042 562.989i 0.0822298 0.142426i
$$251$$ 3245.53 0.816160 0.408080 0.912946i $$-0.366198\pi$$
0.408080 + 0.912946i $$0.366198\pi$$
$$252$$ 0 0
$$253$$ 4486.90 1.11498
$$254$$ 2013.00 3486.62i 0.497271 0.861299i
$$255$$ 0 0
$$256$$ 2484.63 + 4303.50i 0.606598 + 1.05066i
$$257$$ −1776.10 3076.29i −0.431089 0.746668i 0.565878 0.824489i $$-0.308537\pi$$
−0.996967 + 0.0778206i $$0.975204\pi$$
$$258$$ 0 0
$$259$$ 4119.11 7134.51i 0.988220 1.71165i
$$260$$ 6227.59 1.48546
$$261$$ 0 0
$$262$$ −6313.81 −1.48881
$$263$$ −2208.29 + 3824.88i −0.517754 + 0.896776i 0.482033 + 0.876153i $$0.339898\pi$$
−0.999787 + 0.0206232i $$0.993435\pi$$
$$264$$ 0 0
$$265$$ −799.913 1385.49i −0.185427 0.321170i
$$266$$ −6625.89 11476.4i −1.52729 2.64534i
$$267$$ 0 0
$$268$$ −1865.43 + 3231.01i −0.425183 + 0.736439i
$$269$$ −3419.93 −0.775155 −0.387578 0.921837i $$-0.626688\pi$$
−0.387578 + 0.921837i $$0.626688\pi$$
$$270$$ 0 0
$$271$$ 716.407 0.160585 0.0802927 0.996771i $$-0.474415\pi$$
0.0802927 + 0.996771i $$0.474415\pi$$
$$272$$ −4990.56 + 8643.91i −1.11249 + 1.92689i
$$273$$ 0 0
$$274$$ −5981.15 10359.7i −1.31874 2.28412i
$$275$$ 362.298 + 627.519i 0.0794451 + 0.137603i
$$276$$ 0 0
$$277$$ −328.764 + 569.437i −0.0713124 + 0.123517i −0.899477 0.436969i $$-0.856052\pi$$
0.828164 + 0.560485i $$0.189385\pi$$
$$278$$ −7051.72 −1.52135
$$279$$ 0 0
$$280$$ −7009.49 −1.49606
$$281$$ −756.957 + 1311.09i −0.160698 + 0.278338i −0.935119 0.354333i $$-0.884708\pi$$
0.774421 + 0.632671i $$0.218041\pi$$
$$282$$ 0 0
$$283$$ −1953.19 3383.03i −0.410266 0.710601i 0.584653 0.811284i $$-0.301231\pi$$
−0.994919 + 0.100682i $$0.967897\pi$$
$$284$$ −4056.58 7026.20i −0.847584 1.46806i
$$285$$ 0 0
$$286$$ −4928.44 + 8536.31i −1.01897 + 1.76491i
$$287$$ −4781.91 −0.983509
$$288$$ 0 0
$$289$$ −265.611 −0.0540629
$$290$$ −2673.90 + 4631.32i −0.541436 + 0.937795i
$$291$$ 0 0
$$292$$ −8849.16 15327.2i −1.77349 3.07177i
$$293$$ 4024.38 + 6970.43i 0.802413 + 1.38982i 0.918024 + 0.396525i $$0.129784\pi$$
−0.115611 + 0.993295i $$0.536883\pi$$
$$294$$ 0 0
$$295$$ 1076.53 1864.60i 0.212467 0.368004i
$$296$$ −19396.4 −3.80877
$$297$$ 0 0
$$298$$ 1351.37 0.262693
$$299$$ −5061.55 + 8766.87i −0.978987 + 1.69566i
$$300$$ 0 0
$$301$$ −4085.78 7076.78i −0.782394 1.35515i
$$302$$ 1321.76 + 2289.35i 0.251850 + 0.436217i
$$303$$ 0 0
$$304$$ −7644.44 + 13240.6i −1.44223 + 2.49802i
$$305$$ −2972.91 −0.558125
$$306$$ 0 0
$$307$$ 101.564 0.0188814 0.00944068 0.999955i $$-0.496995\pi$$
0.00944068 + 0.999955i $$0.496995\pi$$
$$308$$ 6735.44 11666.1i 1.24606 2.15824i
$$309$$ 0 0
$$310$$ −237.277 410.975i −0.0434723 0.0752962i
$$311$$ 3842.29 + 6655.05i 0.700567 + 1.21342i 0.968268 + 0.249916i $$0.0804030\pi$$
−0.267700 + 0.963502i $$0.586264\pi$$
$$312$$ 0 0
$$313$$ 672.575 1164.93i 0.121457 0.210370i −0.798885 0.601484i $$-0.794577\pi$$
0.920343 + 0.391113i $$0.127910\pi$$
$$314$$ −121.202 −0.0217830
$$315$$ 0 0
$$316$$ 465.310 0.0828346
$$317$$ −3811.17 + 6601.13i −0.675257 + 1.16958i 0.301137 + 0.953581i $$0.402634\pi$$
−0.976394 + 0.215998i $$0.930699\pi$$
$$318$$ 0 0
$$319$$ −2980.38 5162.17i −0.523101 0.906037i
$$320$$ 995.991 + 1725.11i 0.173993 + 0.301364i
$$321$$ 0 0
$$322$$ 9822.74 17013.5i 1.70000 2.94449i
$$323$$ 7118.78 1.22631
$$324$$ 0 0
$$325$$ −1634.80 −0.279022
$$326$$ 10484.8 18160.2i 1.78129 3.08528i
$$327$$ 0 0
$$328$$ 5629.37 + 9750.36i 0.947653 + 1.64138i
$$329$$ 61.0519 + 105.745i 0.0102307 + 0.0177201i
$$330$$ 0 0
$$331$$ 3292.54 5702.85i 0.546751 0.947000i −0.451744 0.892148i $$-0.649198\pi$$
0.998494 0.0548525i $$-0.0174689\pi$$
$$332$$ −10397.0 −1.71870
$$333$$ 0 0
$$334$$ −3494.39 −0.572468
$$335$$ 489.691 848.170i 0.0798647 0.138330i
$$336$$ 0 0
$$337$$ 1473.47 + 2552.13i 0.238175 + 0.412532i 0.960191 0.279345i $$-0.0901174\pi$$
−0.722015 + 0.691877i $$0.756784\pi$$
$$338$$ −5406.36 9364.10i −0.870022 1.50692i
$$339$$ 0 0
$$340$$ 3246.16 5622.52i 0.517788 0.896835i
$$341$$ 528.947 0.0840002
$$342$$ 0 0
$$343$$ −2210.14 −0.347919
$$344$$ −9619.76 + 16661.9i −1.50774 + 2.61148i
$$345$$ 0 0
$$346$$ −4247.72 7357.26i −0.659996 1.14315i
$$347$$ −4246.74 7355.57i −0.656994 1.13795i −0.981390 0.192025i $$-0.938494\pi$$
0.324396 0.945921i $$-0.394839\pi$$
$$348$$ 0 0
$$349$$ −2823.27 + 4890.05i −0.433027 + 0.750024i −0.997132 0.0756785i $$-0.975888\pi$$
0.564106 + 0.825703i $$0.309221\pi$$
$$350$$ 3172.58 0.484519
$$351$$ 0 0
$$352$$ −8748.03 −1.32464
$$353$$ 610.966 1058.22i 0.0921202 0.159557i −0.816283 0.577652i $$-0.803969\pi$$
0.908403 + 0.418096i $$0.137302\pi$$
$$354$$ 0 0
$$355$$ 1064.89 + 1844.44i 0.159207 + 0.275754i
$$356$$ 801.242 + 1387.79i 0.119286 + 0.206609i
$$357$$ 0 0
$$358$$ −887.390 + 1537.00i −0.131006 + 0.226908i
$$359$$ −4151.44 −0.610319 −0.305160 0.952301i $$-0.598710\pi$$
−0.305160 + 0.952301i $$0.598710\pi$$
$$360$$ 0 0
$$361$$ 4045.41 0.589796
$$362$$ 4409.96 7638.28i 0.640283 1.10900i
$$363$$ 0 0
$$364$$ 15196.2 + 26320.5i 2.18817 + 3.79003i
$$365$$ 2322.98 + 4023.52i 0.333125 + 0.576989i
$$366$$ 0 0
$$367$$ 3519.36 6095.70i 0.500569 0.867011i −0.499430 0.866354i $$-0.666457\pi$$
1.00000 0.000657484i $$-0.000209284\pi$$
$$368$$ −22665.5 −3.21065
$$369$$ 0 0
$$370$$ 8779.08 1.23352
$$371$$ 3903.79 6761.56i 0.546293 0.946207i
$$372$$ 0 0
$$373$$ 3559.78 + 6165.72i 0.494152 + 0.855896i 0.999977 0.00674002i $$-0.00214543\pi$$
−0.505826 + 0.862636i $$0.668812\pi$$
$$374$$ 5137.95 + 8899.20i 0.710367 + 1.23039i
$$375$$ 0 0
$$376$$ 143.744 248.971i 0.0197154 0.0341482i
$$377$$ 13448.4 1.83720
$$378$$ 0 0
$$379$$ 3372.29 0.457053 0.228526 0.973538i $$-0.426609\pi$$
0.228526 + 0.973538i $$0.426609\pi$$
$$380$$ 4972.41 8612.47i 0.671261 1.16266i
$$381$$ 0 0
$$382$$ 1889.02 + 3271.87i 0.253012 + 0.438229i
$$383$$ −1979.32 3428.28i −0.264069 0.457381i 0.703250 0.710942i $$-0.251731\pi$$
−0.967319 + 0.253562i $$0.918398\pi$$
$$384$$ 0 0
$$385$$ −1768.11 + 3062.46i −0.234056 + 0.405396i
$$386$$ 22088.6 2.91264
$$387$$ 0 0
$$388$$ 15763.5 2.06256
$$389$$ −4827.00 + 8360.61i −0.629148 + 1.08972i 0.358574 + 0.933501i $$0.383263\pi$$
−0.987723 + 0.156216i $$0.950070\pi$$
$$390$$ 0 0
$$391$$ 5276.72 + 9139.55i 0.682494 + 1.18211i
$$392$$ −7251.13 12559.3i −0.934279 1.61822i
$$393$$ 0 0
$$394$$ −6965.04 + 12063.8i −0.890594 + 1.54255i
$$395$$ −122.148 −0.0155593
$$396$$ 0 0
$$397$$ 10928.3 1.38155 0.690776 0.723068i $$-0.257269\pi$$
0.690776 + 0.723068i $$0.257269\pi$$
$$398$$ −3865.35 + 6694.99i −0.486816 + 0.843189i
$$399$$ 0 0
$$400$$ −1830.14 3169.90i −0.228768 0.396237i
$$401$$ −2042.78 3538.21i −0.254393 0.440622i 0.710337 0.703862i $$-0.248542\pi$$
−0.964731 + 0.263239i $$0.915209\pi$$
$$402$$ 0 0
$$403$$ −596.691 + 1033.50i −0.0737551 + 0.127748i
$$404$$ 15686.6 1.93178
$$405$$ 0 0
$$406$$ −26098.7 −3.19028
$$407$$ −4892.67 + 8474.35i −0.595874 + 1.03208i
$$408$$ 0 0
$$409$$ −5078.13 8795.57i −0.613930 1.06336i −0.990571 0.136998i $$-0.956255\pi$$
0.376642 0.926359i $$-0.377079\pi$$
$$410$$ −2547.93 4413.14i −0.306910 0.531584i
$$411$$ 0 0
$$412$$ −11153.8 + 19319.0i −1.33376 + 2.31014i
$$413$$ 10507.5 1.25191
$$414$$ 0 0
$$415$$ 2729.29 0.322833
$$416$$ 9868.43 17092.6i 1.16308 2.01451i
$$417$$ 0 0
$$418$$ 7870.22 + 13631.6i 0.920921 + 1.59508i
$$419$$ −7939.41 13751.5i −0.925693 1.60335i −0.790443 0.612536i $$-0.790149\pi$$
−0.135250 0.990811i $$-0.543184\pi$$
$$420$$ 0 0
$$421$$ 1139.92 1974.40i 0.131963 0.228567i −0.792470 0.609911i $$-0.791205\pi$$
0.924433 + 0.381344i $$0.124539\pi$$
$$422$$ −25105.8 −2.89604
$$423$$ 0 0
$$424$$ −18382.5 −2.10551
$$425$$ −852.147 + 1475.96i −0.0972593 + 0.168458i
$$426$$ 0 0
$$427$$ −7254.29 12564.8i −0.822154 1.42401i
$$428$$ −9744.51 16878.0i −1.10051 1.90614i
$$429$$ 0 0
$$430$$ 4354.03 7541.39i 0.488302 0.845763i
$$431$$ −1947.38 −0.217638 −0.108819 0.994062i $$-0.534707\pi$$
−0.108819 + 0.994062i $$0.534707\pi$$
$$432$$ 0 0
$$433$$ 12636.2 1.40244 0.701219 0.712946i $$-0.252639\pi$$
0.701219 + 0.712946i $$0.252639\pi$$
$$434$$ 1157.97 2005.67i 0.128075 0.221832i
$$435$$ 0 0
$$436$$ 3844.12 + 6658.22i 0.422248 + 0.731355i
$$437$$ 8082.78 + 13999.8i 0.884787 + 1.53250i
$$438$$ 0 0
$$439$$ 7924.92 13726.4i 0.861585 1.49231i −0.00881399 0.999961i $$-0.502806\pi$$
0.870399 0.492347i $$-0.163861\pi$$
$$440$$ 8325.86 0.902090
$$441$$ 0 0
$$442$$ −23184.0 −2.49491
$$443$$ 8727.78 15117.0i 0.936048 1.62128i 0.163294 0.986577i $$-0.447788\pi$$
0.772754 0.634706i $$-0.218879\pi$$
$$444$$ 0 0
$$445$$ −210.333 364.308i −0.0224062 0.0388086i
$$446$$ −7214.59 12496.0i −0.765965 1.32669i
$$447$$ 0 0
$$448$$ −4860.70 + 8418.99i −0.512604 + 0.887857i
$$449$$ −16068.1 −1.68887 −0.844435 0.535658i $$-0.820064\pi$$
−0.844435 + 0.535658i $$0.820064\pi$$
$$450$$ 0 0
$$451$$ 5679.94 0.593033
$$452$$ −10306.4 + 17851.1i −1.07250 + 1.85762i
$$453$$ 0 0
$$454$$ 13265.2 + 22976.0i 1.37129 + 2.37515i
$$455$$ −3989.13 6909.37i −0.411018 0.711904i
$$456$$ 0 0
$$457$$ −5945.86 + 10298.5i −0.608612 + 1.05415i 0.382858 + 0.923807i $$0.374940\pi$$
−0.991469 + 0.130339i $$0.958393\pi$$
$$458$$ −21311.4 −2.17428
$$459$$ 0 0
$$460$$ 14743.0 1.49434
$$461$$ 1401.11 2426.80i 0.141554 0.245179i −0.786528 0.617555i $$-0.788123\pi$$
0.928082 + 0.372376i $$0.121457\pi$$
$$462$$ 0 0
$$463$$ 6466.66 + 11200.6i 0.649096 + 1.12427i 0.983339 + 0.181780i $$0.0581859\pi$$
−0.334244 + 0.942487i $$0.608481\pi$$
$$464$$ 15055.3 + 26076.6i 1.50631 + 2.60900i
$$465$$ 0 0
$$466$$ −929.915 + 1610.66i −0.0924409 + 0.160112i
$$467$$ 5748.11 0.569573 0.284787 0.958591i $$-0.408077\pi$$
0.284787 + 0.958591i $$0.408077\pi$$
$$468$$ 0 0
$$469$$ 4779.65 0.470583
$$470$$ −65.0602 + 112.688i −0.00638511 + 0.0110593i
$$471$$ 0 0
$$472$$ −12369.6 21424.9i −1.20627 2.08932i
$$473$$ 4853.09 + 8405.79i 0.471766 + 0.817122i
$$474$$ 0 0
$$475$$ −1305.30 + 2260.85i −0.126087 + 0.218389i
$$476$$ 31684.3 3.05094
$$477$$ 0 0
$$478$$ −1828.98 −0.175012
$$479$$ 5608.66 9714.48i 0.535002 0.926651i −0.464161 0.885751i $$-0.653644\pi$$
0.999163 0.0409004i $$-0.0130226\pi$$
$$480$$ 0 0
$$481$$ −11038.6 19119.4i −1.04640 1.81241i
$$482$$ 16032.4 + 27769.0i 1.51506 + 2.62416i
$$483$$ 0 0
$$484$$ 4675.42 8098.06i 0.439089 0.760524i
$$485$$ −4138.07 −0.387423
$$486$$ 0 0
$$487$$ −8905.12 −0.828603 −0.414301 0.910140i $$-0.635974\pi$$
−0.414301 + 0.910140i $$0.635974\pi$$
$$488$$ −17079.8 + 29583.1i −1.58436 + 2.74419i
$$489$$ 0 0
$$490$$ 3281.95 + 5684.51i 0.302579 + 0.524082i
$$491$$ 3276.55 + 5675.15i 0.301158 + 0.521621i 0.976399 0.215976i $$-0.0692934\pi$$
−0.675240 + 0.737598i $$0.735960\pi$$
$$492$$ 0 0
$$493$$ 7010.03 12141.7i 0.640397 1.10920i
$$494$$ −35512.8 −3.23440
$$495$$ 0 0
$$496$$ −2671.96 −0.241884
$$497$$ −5196.94 + 9001.37i −0.469044 + 0.812407i
$$498$$ 0 0
$$499$$ 2305.04 + 3992.45i 0.206789 + 0.358170i 0.950701 0.310108i $$-0.100365\pi$$
−0.743912 + 0.668278i $$0.767032\pi$$
$$500$$ 1190.44 + 2061.90i 0.106476 + 0.184422i
$$501$$ 0 0
$$502$$ −8439.47 + 14617.6i −0.750343 + 1.29963i
$$503$$ 13069.1 1.15850 0.579249 0.815151i $$-0.303346\pi$$
0.579249 + 0.815151i $$0.303346\pi$$
$$504$$ 0 0
$$505$$ −4117.88 −0.362858
$$506$$ −11667.4 + 20208.6i −1.02506 + 1.77546i
$$507$$ 0 0
$$508$$ 7372.43 + 12769.4i 0.643895 + 1.11526i
$$509$$ −7965.40 13796.5i −0.693635 1.20141i −0.970639 0.240542i $$-0.922675\pi$$
0.277004 0.960869i $$-0.410659\pi$$
$$510$$ 0 0
$$511$$ −11336.8 + 19635.9i −0.981428 + 1.69988i
$$512$$ −23102.1 −1.99410
$$513$$ 0 0
$$514$$ 18473.8 1.58530
$$515$$ 2927.97 5071.40i 0.250528 0.433927i
$$516$$ 0 0
$$517$$ −72.5174 125.604i −0.00616888 0.0106848i
$$518$$ 21422.1 + 37104.2i 1.81705 + 3.14723i
$$519$$ 0 0
$$520$$ −9392.19 + 16267.7i −0.792067 + 1.37190i
$$521$$ 3654.38 0.307296 0.153648 0.988126i $$-0.450898\pi$$
0.153648 + 0.988126i $$0.450898\pi$$
$$522$$ 0 0
$$523$$ −5138.66 −0.429633 −0.214816 0.976654i $$-0.568915\pi$$
−0.214816 + 0.976654i $$0.568915\pi$$
$$524$$ 11561.9 20025.7i 0.963898 1.66952i
$$525$$ 0 0
$$526$$ −11484.6 19891.9i −0.952002 1.64892i
$$527$$ 622.057 + 1077.43i 0.0514179 + 0.0890584i
$$528$$ 0 0
$$529$$ −5899.05 + 10217.5i −0.484840 + 0.839768i
$$530$$ 8320.16 0.681896
$$531$$ 0 0
$$532$$ 48533.4 3.95524
$$533$$ −6407.39 + 11097.9i −0.520704 + 0.901885i
$$534$$ 0 0
$$535$$ 2558.02 + 4430.62i 0.206716 + 0.358042i
$$536$$ −5626.71 9745.75i −0.453427 0.785359i
$$537$$ 0 0
$$538$$ 8892.96 15403.1i 0.712645 1.23434i
$$539$$ −7316.27 −0.584664
$$540$$ 0 0
$$541$$ 6932.06 0.550892 0.275446 0.961317i $$-0.411175\pi$$
0.275446 + 0.961317i $$0.411175\pi$$
$$542$$ −1862.90 + 3226.64i −0.147635 + 0.255712i
$$543$$ 0 0
$$544$$ −10287.9 17819.2i −0.810831 1.40440i
$$545$$ −1009.12 1747.84i −0.0793134 0.137375i
$$546$$ 0 0
$$547$$ 1711.56 2964.50i 0.133786 0.231724i −0.791347 0.611367i $$-0.790620\pi$$
0.925133 + 0.379643i $$0.123953\pi$$
$$548$$ 43810.8 3.41516
$$549$$ 0 0
$$550$$ −3768.39 −0.292154
$$551$$ 10737.8 18598.4i 0.830211 1.43797i
$$552$$ 0 0
$$553$$ −298.058 516.251i −0.0229199 0.0396984i
$$554$$ −1709.79 2961.45i −0.131123 0.227112i
$$555$$ 0 0
$$556$$ 12913.1 22366.2i 0.984962 1.70600i
$$557$$ −24489.2 −1.86291 −0.931455 0.363856i $$-0.881460\pi$$
−0.931455 + 0.363856i $$0.881460\pi$$
$$558$$ 0 0
$$559$$ −21898.6 −1.65691
$$560$$ 8931.59 15470.0i 0.673979 1.16737i
$$561$$ 0 0
$$562$$ −3936.68 6818.54i −0.295479 0.511784i
$$563$$ 5026.54 + 8706.22i 0.376276 + 0.651729i 0.990517 0.137389i $$-0.0438711\pi$$
−0.614241 + 0.789118i $$0.710538\pi$$
$$564$$ 0 0
$$565$$ 2705.51 4686.08i 0.201454 0.348929i
$$566$$ 20315.8 1.50872
$$567$$ 0 0
$$568$$ 24471.8 1.80777
$$569$$ 3335.23 5776.78i 0.245729 0.425616i −0.716607 0.697477i $$-0.754306\pi$$
0.962336 + 0.271861i $$0.0876392\pi$$
$$570$$ 0 0
$$571$$ −2316.78 4012.77i −0.169797 0.294097i 0.768551 0.639788i $$-0.220978\pi$$
−0.938348 + 0.345691i $$0.887645\pi$$
$$572$$ −18050.0 31263.5i −1.31942 2.28530i
$$573$$ 0 0
$$574$$ 12434.6 21537.3i 0.904196 1.56611i
$$575$$ −3870.17 −0.280691
$$576$$ 0 0
$$577$$ 7045.15 0.508307 0.254154 0.967164i $$-0.418203\pi$$
0.254154 + 0.967164i $$0.418203\pi$$
$$578$$ 690.677 1196.29i 0.0497031 0.0860883i
$$579$$ 0 0
$$580$$ −9792.89 16961.8i −0.701082 1.21431i
$$581$$ 6659.84 + 11535.2i 0.475554 + 0.823683i
$$582$$ 0 0
$$583$$ −4636.91 + 8031.37i −0.329402 + 0.570541i
$$584$$ 53383.7 3.78259
$$585$$ 0 0
$$586$$ −41859.0 −2.95082
$$587$$ 4000.53 6929.12i 0.281294 0.487216i −0.690410 0.723419i $$-0.742570\pi$$
0.971704 + 0.236203i $$0.0759030\pi$$
$$588$$ 0 0
$$589$$ 952.855 + 1650.39i 0.0666582 + 0.115455i
$$590$$ 5598.66 + 9697.16i 0.390666 + 0.676654i
$$591$$ 0 0
$$592$$ 24715.2 42808.0i 1.71586 2.97196i
$$593$$ 6747.53 0.467265 0.233632 0.972325i $$-0.424939\pi$$
0.233632 + 0.972325i $$0.424939\pi$$
$$594$$ 0 0
$$595$$ −8317.41 −0.573077
$$596$$ −2474.63 + 4286.19i −0.170075 + 0.294579i
$$597$$ 0 0
$$598$$ −26323.5 45593.6i −1.80008 3.11783i
$$599$$ −10773.6 18660.5i −0.734890 1.27287i −0.954771 0.297341i $$-0.903900\pi$$
0.219881 0.975527i $$-0.429433\pi$$
$$600$$ 0 0
$$601$$ 6077.53 10526.6i 0.412492 0.714456i −0.582670 0.812709i $$-0.697992\pi$$
0.995162 + 0.0982525i $$0.0313253\pi$$
$$602$$ 42497.6 2.87720
$$603$$ 0 0
$$604$$ −9681.64 −0.652219
$$605$$ −1227.34 + 2125.81i −0.0824767 + 0.142854i
$$606$$ 0 0
$$607$$ −8174.47 14158.6i −0.546608 0.946754i −0.998504 0.0546827i $$-0.982585\pi$$
0.451895 0.892071i $$-0.350748\pi$$
$$608$$ −15758.9 27295.2i −1.05116 1.82067i
$$609$$ 0 0
$$610$$ 7730.55 13389.7i 0.513116 0.888743i
$$611$$ 327.220 0.0216660
$$612$$ 0 0
$$613$$ −29955.5 −1.97372 −0.986859 0.161581i $$-0.948341\pi$$
−0.986859 + 0.161581i $$0.948341\pi$$
$$614$$ −264.101 + 457.437i −0.0173587 + 0.0300662i
$$615$$ 0 0
$$616$$ 20316.2 + 35188.7i 1.32884 + 2.30161i
$$617$$ −1079.87 1870.39i −0.0704603 0.122041i 0.828643 0.559778i $$-0.189113\pi$$
−0.899103 + 0.437737i $$0.855780\pi$$
$$618$$ 0 0
$$619$$ −11050.4 + 19139.9i −0.717535 + 1.24281i 0.244439 + 0.969665i $$0.421396\pi$$
−0.961974 + 0.273142i $$0.911937\pi$$
$$620$$ 1738.01 0.112581
$$621$$ 0 0
$$622$$ −39965.0 −2.57629
$$623$$ 1026.48 1777.92i 0.0660114 0.114335i
$$624$$ 0 0
$$625$$ −312.500 541.266i −0.0200000 0.0346410i
$$626$$ 3497.84 + 6058.44i 0.223326 + 0.386811i
$$627$$ 0 0
$$628$$ 221.946 384.422i 0.0141029 0.0244269i
$$629$$ −23015.7 −1.45898
$$630$$ 0 0
$$631$$ 18360.1 1.15833 0.579164 0.815211i $$-0.303379\pi$$
0.579164 + 0.815211i $$0.303379\pi$$
$$632$$ −701.761 + 1215.49i −0.0441686 + 0.0765023i
$$633$$ 0 0
$$634$$ −19820.6 34330.3i −1.24160 2.15052i
$$635$$ −1935.33 3352.09i −0.120947 0.209486i
$$636$$ 0 0
$$637$$ 8253.29 14295.1i 0.513355 0.889157i
$$638$$ 30999.9 1.92367
$$639$$ 0 0
$$640$$ 1713.32 0.105820
$$641$$ 10532.3 18242.4i 0.648985 1.12407i −0.334381 0.942438i $$-0.608527\pi$$
0.983366 0.181636i $$-0.0581393\pi$$
$$642$$ 0 0
$$643$$ 5269.57 + 9127.16i 0.323190 + 0.559782i 0.981144 0.193276i $$-0.0619112\pi$$
−0.657954 + 0.753058i $$0.728578\pi$$
$$644$$ 35974.9 + 62310.3i 2.20126 + 3.81269i
$$645$$ 0 0
$$646$$ −18511.2 + 32062.4i −1.12742 + 1.95275i
$$647$$ 22553.4 1.37043 0.685213 0.728343i $$-0.259709\pi$$
0.685213 + 0.728343i $$0.259709\pi$$
$$648$$ 0 0
$$649$$ −12480.8 −0.754873
$$650$$ 4251.02 7362.99i 0.256521 0.444308i
$$651$$ 0 0
$$652$$ 38399.7 + 66510.2i 2.30652 + 3.99500i
$$653$$ −11312.0 19593.0i −0.677908 1.17417i −0.975610 0.219512i $$-0.929554\pi$$
0.297702 0.954659i $$-0.403780\pi$$
$$654$$ 0 0
$$655$$ −3035.09 + 5256.94i −0.181055 + 0.313596i
$$656$$ −28692.1 −1.70768
$$657$$ 0 0
$$658$$ −635.022 −0.0376227
$$659$$ −3188.30 + 5522.29i −0.188465 + 0.326431i −0.944739 0.327824i $$-0.893685\pi$$
0.756274 + 0.654255i $$0.227018\pi$$
$$660$$ 0 0
$$661$$ 11048.8 + 19137.0i 0.650146 + 1.12609i 0.983087 + 0.183139i $$0.0586258\pi$$
−0.332941 + 0.942948i $$0.608041\pi$$
$$662$$ 17123.4 + 29658.7i 1.00532 + 1.74126i
$$663$$ 0 0
$$664$$ 15680.2 27159.0i 0.916433 1.58731i
$$665$$ −12740.4 −0.742938
$$666$$ 0 0
$$667$$ 31837.2 1.84819
$$668$$ 6398.93 11083.3i 0.370632 0.641953i
$$669$$ 0 0
$$670$$ 2546.72 + 4411.05i 0.146848 + 0.254349i
$$671$$ 8616.63 + 14924.4i 0.495740 + 0.858646i
$$672$$ 0 0
$$673$$ −12016.5 + 20813.2i −0.688264 + 1.19211i 0.284136 + 0.958784i $$0.408293\pi$$
−0.972399 + 0.233323i $$0.925040\pi$$
$$674$$ −15326.1 −0.875873
$$675$$ 0 0
$$676$$ 39600.6 2.25311
$$677$$ −89.8191 + 155.571i −0.00509901 + 0.00883175i −0.868564 0.495578i $$-0.834956\pi$$
0.863465 + 0.504409i $$0.168290\pi$$
$$678$$ 0 0
$$679$$ −10097.4 17489.3i −0.570698 0.988478i
$$680$$ 9791.45 + 16959.3i 0.552184 + 0.956411i
$$681$$ 0 0
$$682$$ −1375.44 + 2382.33i −0.0772262 + 0.133760i
$$683$$ −30434.2 −1.70502 −0.852511 0.522709i $$-0.824921\pi$$
−0.852511 + 0.522709i $$0.824921\pi$$
$$684$$ 0 0
$$685$$ −11500.7 −0.641490
$$686$$ 5747.11 9954.28i 0.319862 0.554018i
$$687$$ 0 0
$$688$$ −24515.3 42461.7i −1.35848 2.35296i
$$689$$ −10461.6 18120.0i −0.578453 1.00191i
$$690$$ 0 0
$$691$$ −4896.36 + 8480.75i −0.269561 + 0.466893i −0.968748 0.248045i $$-0.920212\pi$$
0.699188 + 0.714938i $$0.253545\pi$$
$$692$$ 31113.7 1.70920
$$693$$ 0 0
$$694$$ 44171.8 2.41605
$$695$$ −3389.81 + 5871.33i −0.185011 + 0.320449i
$$696$$ 0 0
$$697$$ 6679.78 + 11569.7i 0.363005 + 0.628743i
$$698$$ −14682.9 25431.5i −0.796212 1.37908i
$$699$$ 0 0
$$700$$ −5809.65 + 10062.6i −0.313691 + 0.543329i
$$701$$ 8130.47 0.438065 0.219032 0.975718i $$-0.429710\pi$$
0.219032 + 0.975718i $$0.429710\pi$$
$$702$$ 0 0
$$703$$ −35255.0 −1.89142
$$704$$ 5773.54 10000.1i 0.309089 0.535357i
$$705$$ 0 0
$$706$$ 3177.43 + 5503.47i 0.169383 + 0.293379i
$$707$$ −10048.2 17404.0i −0.534513 0.925804i
$$708$$ 0 0
$$709$$ 2429.98 4208.84i 0.128716 0.222943i −0.794463 0.607312i $$-0.792248\pi$$
0.923179 + 0.384369i $$0.125581\pi$$
$$710$$ −11076.3 −0.585472
$$711$$ 0 0
$$712$$ −4833.59 −0.254419
$$713$$ −1412.59 + 2446.67i −0.0741961 + 0.128511i
$$714$$ 0 0
$$715$$ 4738.28 + 8206.94i 0.247834 + 0.429262i
$$716$$ −3249.98 5629.13i −0.169633 0.293814i
$$717$$ 0 0
$$718$$ 10795.1 18697.7i 0.561101 0.971856i
$$719$$ 19463.0 1.00952 0.504762 0.863259i $$-0.331580\pi$$
0.504762 + 0.863259i $$0.331580\pi$$
$$720$$ 0 0
$$721$$ 28578.6 1.47618
$$722$$ −10519.4 + 18220.2i −0.542233 + 0.939175i
$$723$$ 0 0
$$724$$ 16151.1 + 27974.5i 0.829075 + 1.43600i
$$725$$ 2570.72 + 4452.62i 0.131689 + 0.228091i
$$726$$ 0 0
$$727$$ −1216.33 + 2106.75i −0.0620512 + 0.107476i −0.895382 0.445299i $$-0.853098\pi$$
0.833331 + 0.552774i $$0.186431\pi$$
$$728$$ −91672.8 −4.66706
$$729$$ 0 0
$$730$$ −24162.1 −1.22504
$$731$$ −11414.7 + 19770.9i −0.577551 + 1.00035i
$$732$$ 0 0
$$733$$ 8983.79 + 15560.4i 0.452693 + 0.784087i 0.998552 0.0537895i $$-0.0171300\pi$$
−0.545859 + 0.837877i $$0.683797\pi$$
$$734$$ 18303.0 + 31701.8i 0.920404 + 1.59419i
$$735$$ 0 0
$$736$$ 23362.2 40464.5i 1.17003 2.02655i
$$737$$ −5677.26 −0.283751
$$738$$ 0 0
$$739$$ 23473.0 1.16843 0.584214 0.811599i $$-0.301403\pi$$
0.584214 + 0.811599i $$0.301403\pi$$
$$740$$ −16076.3 + 27844.9i −0.798616 + 1.38324i
$$741$$ 0 0
$$742$$ 20302.3 + 35164.6i 1.00448 + 1.73980i
$$743$$ 16779.6 + 29063.2i 0.828512 + 1.43503i 0.899205 + 0.437527i $$0.144146\pi$$
−0.0706932 + 0.997498i $$0.522521\pi$$
$$744$$ 0 0
$$745$$ 649.613 1125.16i 0.0319463 0.0553325i
$$746$$ −37026.5 −1.81721
$$747$$ 0 0
$$748$$ −37634.6 −1.83965
$$749$$ −12483.8 + 21622.6i −0.609011 + 1.05484i
$$750$$ 0 0
$$751$$ 3891.38 + 6740.06i 0.189079 + 0.327495i 0.944943 0.327234i $$-0.106116\pi$$
−0.755864 + 0.654728i $$0.772783\pi$$
$$752$$ 366.320 + 634.485i 0.0177637 + 0.0307677i
$$753$$ 0 0
$$754$$ −34970.2 + 60570.2i −1.68905 + 2.92551i
$$755$$ 2541.52 0.122510
$$756$$ 0 0
$$757$$ −38154.3 −1.83189 −0.915946 0.401300i $$-0.868558\pi$$
−0.915946 + 0.401300i $$0.868558\pi$$
$$758$$ −8769.09 + 15188.5i −0.420195 + 0.727799i
$$759$$ 0 0
$$760$$ 14998.4 + 25977.9i 0.715852 + 1.23989i
$$761$$ −9933.56 17205.4i −0.473182 0.819575i 0.526347 0.850270i $$-0.323561\pi$$
−0.999529 + 0.0306951i $$0.990228\pi$$
$$762$$ 0 0
$$763$$ 4924.76 8529.93i 0.233667 0.404724i
$$764$$ −13836.7 −0.655228
$$765$$ 0 0
$$766$$ 20587.5 0.971094
$$767$$ 14079.2 24385.9i 0.662805 1.14801i
$$768$$ 0 0
$$769$$ 7855.40 + 13605.9i 0.368365 + 0.638027i 0.989310 0.145827i $$-0.0465843\pi$$
−0.620945 + 0.783854i $$0.713251\pi$$
$$770$$ −9195.37 15926.9i −0.430361 0.745408i
$$771$$ 0 0
$$772$$ −40448.7 + 70059.3i −1.88573 + 3.26618i
$$773$$ 25811.9 1.20102 0.600510 0.799617i $$-0.294964\pi$$
0.600510 + 0.799617i $$0.294964\pi$$
$$774$$ 0 0
$$775$$ −456.242 −0.0211467
$$776$$ −23773.9 + 41177.6i −1.09978 + 1.90488i
$$777$$ 0 0
$$778$$ −25103.6 43480.8i −1.15682 2.00368i
$$779$$ 10232.0 + 17722.3i 0.470600 + 0.815104i
$$780$$ 0 0
$$781$$ 6172.92 10691.8i 0.282822 0.489863i
$$782$$ −54885.0 −2.50982
$$783$$ 0 0
$$784$$ 36958.0 1.68358
$$785$$ −58.2629 + 100.914i −0.00264903 +